1. Introduction

Chalcogenide glasses (ChGs) are well-known for their high non-resonant, third-order non-linearity (TONL, χ⁽³⁾) and exceptional optical transmittance in infrared. As such, they have been considered as a promising candidate for the applications in ultra-fast photonic processing devices operated at infrared wavelengths [1–3]. Recently, a number of studies [4–6] have been carried out on the realization of selenium-based ChGs, micro-photonic devices by utilizing their high χ⁽³⁾ (~1000 times that of silica) and flexible forms, e.g. bulk (fiber), thin film, or even solution. However, the research work on both TONL properties and related applications has been limited into a few systems of As−Se or Ge-As-Se based glasses. This is because elements of Ge, As, and Se exhibit very similar atomic structure, thus their melting combination has the advantages of large glass forming region and strong stability against crystallization, while the extreme harm of arsenic to natural environment is totally disregarded.

Arsenic-free and selenium-based ChGs, in particular, the system of Ge−Sb−Se glasses, represent an alternative to the above-said photonic applications. There have been investigations on the optical, physical and thermal properties of Ge−Sb−Se glasses [7–10], which give conclusions that Ge−Sb−Se glasses possess thermal and chemical stabilities comparable to those of As−Se glasses and they also have large glass forming region and exceptional infrared transparence. Besides, according to the Miller’s rule [11], the substitution of arsenic by antimony would promote the TONL of selenium-based ChGs since they are elements of a same category and the latter has larger cation polarizability than that of the former. Lenz et al [12] first reported the TONL parameter of a Ge−Sb−Se glass and found its better performance as compared to As₂Se₃ at 1550 nm. Petit et al [13] characterized the TONL properties of Ge−Sb−Se glasses as well as their evident composition dependence at 1064 nm. Olivier et al [14] recently measured the TONL properties of Ge−Sb−Se glasses with stoichiometry at 1550 nm, and they found that antimony is the key element to the TONL properties of the glasses. Our previous study [15] investigated the TONL dispersion properties of Ge−Sb−Se in the near infrared region, and the decrease of nonlinear refraction with increase of wavelength was observed. The above literatures have well characterized the TONL properties of Ge−Sb−Se glasses at near infrared wavelengths, especially at telecom wavelengths, but for the nonlinear parameters of the chalcogenide glasses at longer wavelengths (mid-infrared and far-infrared regions) that are critical for realization of infrared photonic applications, especially supercontinuum generation, little is known.

In this paper, we report the TONL properties of Ge−Sb−Se glasses at two mid-infrared (MIR) wavelengths (2000 and 2500 nm) by employing femtosecond Z-scan technique. Wavelength and composition dependences of TONL parameters (nonlinear refraction and nonlinear absorption coefficient) of the ChGs are also discussed.

2. Experimental

Molar compositions of the Ge−Sb−Se glasses in this study are all listed in Table 1. For the first eight glass samples (labeled as Gex, x = 7.5, 10, 15, 20, 25, 27.5, 30 and 32.5), we purposely fixed the Sb content to 10 mol% and altered the content of Ge and Se, and they are referred to constant Sb (CSb) glass series. Then, another four glass compositions with more Sb content were selected (labeled as Sbx, x = 15, 20, 23, and 25), and they are referred to various Sb (VSb) glass series. Accordingly, the influence of the three components (Ge, Sb, and Se) on the TONL properties of the glasses can be investigated.

Table 1. Composition, optical band gap (E_opg) and mean coordination number (MCN) of glasses in this study.

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Raw materials of high-purity polycrystalline germanium (5 N), antimony (5 N), and selenium (5 N) were carefully weighed (50 g) and sealed in evacuated (10⁻⁴ Pa) silica glass ampoules, and then kept at 120 °C for 4h to eliminate surface moisture from the materials. The sealed ampoules were then melted at 950 °C in a rocking furnace for 24 h, followed by being quenched in water. In order to reduce stress and improve optical homogeneity, the glasses were annealed at temperature 30 °C below glass transition temperature (T_g) for 2h and cooled down with a rate of 10 °C/h to room temperature. The sample plates of 1 mm thickness were cut and carefully polished for optical measurements reported as follows.

Absorption spectra of the samples were obtained by a Shimadzu (UV-3600) UV-VIS-NIR Spectrophotometer. By using an optical parametric generator (Light Conversion TOPAZ) pumped by an 800 nm Ti:sapphire laser producing ≈150 fs laser pulses at a repetition rate of 1 kHz, Z-scan measurements on the Ge−Sb−Se glasses were carried out at mid-infrared wavelengths of 2000 and 2500 nm as well as telecom wavelength of 1550 nm (for reference), and the incident energy of single laser pulse was kept at 128 ± 10 nJ. The measurements were repeated ten times at different places on the sample surface to minimize experimental error. We define that the nonlinear refraction (γ) as the change in the refractive index divided by the laser intensity; and α₂ (or α₃) is the two-photon (or three-photon) absorption coefficient. By using the well-established fitting procedure [16, 17], both nonlinear refraction (γ) and nonlinear absorption coefficient (α₂ or α₃) of the ChGs were extracted from the best fittings and listed in Table 2. It should be noted that the nonlinear refraction γ value of As₂Se₃ at 1550 nm is estimated to be 1.0 × 10⁻¹⁷ m²/W, in good agreement with the value reported in literatures [18, 19], ensuring the accuracy of present measurements. All of the above optical measurements were conducted at room temperature.

Table 2. Nonlinear optical parameters of the chalcogenide glasses measured at 1550, 2000 and 2500 nm.

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3. Results and Discussion

Figure 1 presents the absorption spectra of the two Ge−Sb−Se glass series and the As₂Se₃ glass. For the CSb glasses, Fig. 1(a) shows that their absorption edge (UV cut-off) blue-shifts as the Ge content reaches 25 mol%, and then significantly red-shifts. Meanwhile, as can be seen in Fig. 1(b), absorption edge of the VSb glasses red-shifted monotonically with increase of Sb content.

 

Fig. 1 Absorption spectra of the CSb glass series (a) and VSb glass series (b) as well as As₂Se₃.

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Since the evolution of absorption edge can be represented by optical band gap (E_opg) [20], E_opg of the Ge−Sb−Se glasses is estimated at the absorption coefficient equals to 1000 cm⁻¹ [9]. As the data listed in Table 1, the maximum E_opg value was obtained from Ge25 in the CSb series. Since this sample is in composition stoichiometry, such observation is in good agreement with Srinivasan’s investigation demonstrating that the bonding energy of Ge−Sb−Se glass network would reach a maximum level in the stoichiometry [10]. For the VSb series, E_opg decreases significantly with increase of Sb content, informing the weakening of total bonding energy with addition of Sb. Further, according to the previous studies on TONL properties of amorphous materials [21, 22], E_opg is a key parameter to multi-photon absorption that contributes to an increase in the imaginary part of χ⁽³⁾, thus it would in turn alter the magnitude of nonlinear refraction (real part of χ⁽³⁾) as explained by the Kramers–Kronig (KK) relations.

TONL properties of the Ge−Sb−Se glass as well as the reference glass (As₂Se₃) were investigated by femtosecond Z-scan technique at 2000 and 2500 nm as well as at telecom wavelength (1550 nm). Figure 2 shows the closed-aperture (CA) and open-aperture (OA) Z-scans of sample Ge20, which qualitatively represents typical behavior in the Z-scan measurements on all the glasses prepared in this study.

 

Fig. 2 CA and OA Z-scans of the ChGs in molar composition of 20Ge−10Sb−70Se at 1550 nm (a) and (d); at 2000 nm (b) and (e); and at 2500 nm (c) and (f), respectively.

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Firstly, all the CA curves exhibit a valley-and-peak configuration, indicating self-focusing, namely positive sign of the glasses at the three testing wavelengths. As the calculation data shown in Table 2, nonlinear refraction γ of glasses in VSb series increases monotonically with increase of Sb content, and the maximum γ value of all glasses in this study was obtained from Sb25, confirming the significant role of Sb on TONL properties of the glasses. However, it is of interest to find that glass samples with Se- and Ge-rich composition in CSb series also have relatively high γ-values, even higher than some samples in the VSb glass series. According to previous studies, various physical properties of ChGs obey the mean coordination numbers (MCNs) theory [9, 23]: MCN < 2.4 represents a ‘floppy’ and weakly-bonded network while MCN > 2.67 represents a ‘stressed-rigid’ region; the region of 2.4 ≤ MCN ≤ 2.67 is termed as the ‘intermediate phase’.

For the present Ge−Sb−Se ternary system, the three elements have different coordination number (CN) in the glasses (CN_Ge = 4, CN_Sb = 3, CN_Se = 2), thus the MCN the CSb glass series of could cover the three regions as Se was replaced by Ge. By plotting γ versus MCN of the CSb glass series, as shown in Fig. 3, two jump points of γ at MCN approaching 2.4 and above 2.7 can be observed, and such MCN values were considered as the threshold for glass network evolution. Our previous study [9] on structural properties of Ge−Sb−Se glasses had shown that the evolution of glass network is related to the formation of homopolar bonds in glass matrix. Large numbers of Se-Se and Ge−Ge homopolar bonds exist in glasses with compositional Se-rich and Ge-rich, which caused the ‘floppy’ and ‘stressed-rigid’ glass network respectively. More importantly, Sb-Sb homopolar bonds would appear in glasses with highly Ge-rich composition. In this study, the relatively large γ values in the CSb series obtained from the Ge-richest sample (Ge32.5) and some Se-rich samples (Ge7.5, Ge10 and Ge15) are associated with the appearance of homopolar bonds in the ChG glasses. In the former case, considering the relatively low γ value of Ge30, the strong nonlinear refraction behavior of Ge32.5 can be attributed to the presence of Sb−Sb homopolar bonds which would be formed only as Ge content of the CSb glasses excesses 30 mol% as demonstrated in our previous study [9], rather than Ge−Ge homopolar bonds which have less possibility to be polarized by irradiation as compared to Sb−Sb bonds for the highest CN value of Ge in the ternary system. Besides, the large γ obtained from Sb23 and Sb25 is also associated with Sb−Sb homopolar bonds which would appear in glasses with Sb content over 20 mol%. For the CSb samples in ‘intermediate phase’ region, namely compositions near stoichiometry, they have relatively lower γ-value as a result of the smaller number of homopolar bonds in these samples. It is in consistence with Prasad’s study that relatively weak linear and nonlinear refraction would occur near the stoichiometry of Ge−As−Se glass system [23]. For the rest of the ChGs with MCN ≤ 2.4, it is of interest to note that all samples (including As₂Se₃ in compositional stoichiometry) have relatively high γ values, informing the large contribution of ‘floppy’ glass network to nonlinear refraction. Therefore, we believe that such glass network is a result of presence of single bond connected Se-Se chains in the glass network, which is extremely flexible and can be easily twisted under laser beam exposure.

 

Fig. 3 Nonlinear refraction (γ) versus mean co-ordination numbers (MCN) of the CSb glass series and As₂Se₃

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On the other hand, the evident asymmetry in CA curve (valley larger than peak) informed the presence of nonlinear absorption of the ChGs, which was confirmed by the downward tendency of optical transmittance (T_OA) in the OA Z-scans. At the MIR wavelengths of 2000 and 2500 nm, the most important experimental result found in OA Z-scans is the presence of three-photon absorption (3PA) [24], which was proved by the slope of 2 of ln(1-T_OA) versus lnI₀ (I₀ is laser irradiance approaching the focus) in Fig. 4. For the OA Z-scans at 1550 nm as present in Fig. 2(d), two-photon absorption (2PA) was observed, which isconsistent with previous studies. As the calculation data shown in Table 2, it is of interest to find the compositional dependence of both nonlinear absorption coefficients (α₂ and α₃) have almost the same tendency to that of the γ values, informing the availability of KK relations in the MIR region as well as the telecom wavelength.

 

Fig. 4 Plotting of ln(1-T_OA) versus lnI₀, slope of 2 confirms three photon absorption.

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Recently, large 3PA was observed in silicon at MIR due to its small energy band gap (E_g) of 1.1 eV [25], which resulted in high 3PA-enhanced nonlinear refraction at the corresponding wavelengths. For the present ChGs, the large 3PA at 2000 nm can be attributed to electron band-to-band transition type since 1/3E_opg of the GhGs is comparable to the hv at 2000 nm (hv = 0.62 eV) and smaller than it, thus nonlinear refraction behaviors of the ChGs at 2000 nm is increased significantly when approaching to the 3PA resonance and the γ values are near two times to those obtained from 1550 nm. As the wavelength goes to 2500 nm, both CA and OA Z-scan signal attenuated as seen in Figs. 2(c) and 2(f), as a result of the small photon energy (hv = 0.5 eV) that is below 1/3E_opg of most of the ChGs, therefore, origination of the 3PA at 2500 nm is defect absorption tail below the band gap, namely from Urbach absorption region. The weak Urbach type 3PA resulted in lower nonlinear refraction by the KK relations; and consequently the smallest γ value among the three testing wavelengths. For samples Sb23 and Sb25, their 1/3E_opg is smaller than the hv of 2500 nm, thus they remain exhibiting large 3PA coefficient (α₃) which is one order higher than those of other ChGs. Besides, it can be seen that As₂Se₃ has relatively high Urbach type α₃, indicating that there are a number of defect structures, namely homopolar bonds in the glass network, although it is in compositional stoichiometry.

Since multi-photon absorption is the main limitation for TONL materials to be applied in photonic devices, such as all-optical switching (AOS) at telecom wavelength and supercontinuum generation at MIR, figure of merit (FOM) is proposed to evaluate their performance at corresponding wavelength (λ) [3]. For 2PA- and 3PA-dominant materials, FOM is γ/(α₂λ) and γ/(α₃λI₀) (I₀ is the laser intensity at focus) respectively, and the values > 10 are desirable for efficient all-optical devices. As the data presented in Table 2, the FOMs at 2000 nm are the largest among the three testing wavelengths, and most of FOMs at 2000 nm and several ones at 2500 nm satisfy the criterion for all-optical devices (FOM > 10). It is of interest to note that relatively large FOM can be obtained from Ge−Sb−Se ChGs near the stoichiometry due to their relatively weak nonlinear absorption, and the maximum value reaches 50 from Ge25 at 2000 nm, indicting its greatest potential to the above mentioned devices.

4. Conclusions

In summary, we have investigated the optical nonlinearities of chalcogenide glasses (ChGs) within Ge−Sb−Se ternary system at mid-infrared (MIR) wavelengths of 2000 and 2500 nm as well as telecom wavelength (1550 nm) by employing femtosecond Z-scan technique. The maximum nonlinear refraction (γ) was obtained from GhG with highest Sb content, thus Sb was considered to be the most important element to the nonlinear properties of the GhGs. Besides, relatively large γ was obtained in GhGs with mean coordination numbers (MCNs) over 2.7 and those with MCNs below 2.4, as a result of the presence of Sb-Sb and Se-Se homopolar bonds, respectively. Large three-photon absorption was observed at 2000 nm, leading to 3PA resonance enhanced γ values which are near two times to those obtained from the shorter wavelength (1550 nm). The maximum figure of merit (50) was obtained from ChGs in stoichiometry at 2000 nm, indicating the great potential of the Ge−Sb−Se GhGs to be applied in photonic devices that operated in the MIR region.